Maximum resistance??

Question

In the picture below R1=2.00Ω and R2=4.00Ω. What value of R3 maximizes the dissipation rate in resistance 3? I worked it all out using Kirchoff’s laws and I got R3 = 10/7Ω. I would like to know if first this is correct and second what would happen if R2 is switched from 4.00Ω to 5.00Ω. I would like to see some work with 5.00 Ω, b/c the answer I keep getting is wrong.

http://www.lowellphysics.org/beta/resources/CH27/Problems/c27x27_11.xform_files/nw0394-n.gif

Answer 1

Max power is transferred when the load resistance R3 = the source resistance. Source resistance is the parallel resistance of R1 & R2, 4/3 ohms.
If R2 = 5 ohms, R3 = 10/7 ohms.